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Representation-of-integers

Integer-from-sllong

Accessor for values of type signed long long.

Signature
(integer-from-sllong x) → y
Arguments: x — Guard (sllongp x).
Returns: y — Type (sllong-integerp y).

Definitions and Theorems

Function: integer-from-sllong

(defun integer-from-sllong (x)
  (declare (xargs :guard (sllongp x)))
  (let ((__function__ 'integer-from-sllong))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (sllong-integer-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: sllong-integerp-of-integer-from-sllong

(defthm sllong-integerp-of-integer-from-sllong
  (b* ((y (integer-from-sllong x)))
    (sllong-integerp y))
  :rule-classes :rewrite)

Theorem: sllong-from-integer-of-integer-from-sllong

(defthm sllong-from-integer-of-integer-from-sllong
  (equal (sllong-from-integer (integer-from-sllong x))
         (sllong-fix x)))

Theorem: integer-from-sllong-of-sllong-from-integer

(defthm integer-from-sllong-of-sllong-from-integer
  (equal (integer-from-sllong (sllong-from-integer get))
         (sllong-integer-fix get)))

Theorem: integer-from-sllong-upper-bound

(defthm integer-from-sllong-upper-bound
  (<= (integer-from-sllong x)
      (sllong-max))
  :rule-classes :linear)

Theorem: integer-from-sllong-lower-bound

(defthm integer-from-sllong-lower-bound
  (>= (integer-from-sllong x)
      (sllong-min))
  :rule-classes :linear)

Theorem: integer-from-sllong-of-sllong-fix-x

(defthm integer-from-sllong-of-sllong-fix-x
  (equal (integer-from-sllong (sllong-fix x))
         (integer-from-sllong x)))

Theorem: integer-from-sllong-sllong-equiv-congruence-on-x

(defthm integer-from-sllong-sllong-equiv-congruence-on-x
  (implies (sllong-equiv x x-equiv)
           (equal (integer-from-sllong x)
                  (integer-from-sllong x-equiv)))
  :rule-classes :congruence)